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329sum09he2sol - MEN/cf!”— ECE 329 Hour Exam 2 1 The...

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Unformatted text preview: MEN/cf?!”— ECE 329 Hour Exam 2 July 17, 2009 1. The region between two infinite, plane parallel, perfectly conducting plates at z = 0 and z = 10 mm is filled with two slabs of perfect dielectric materials having constant electric permittivities 61 = 60 for 0 < z < 5 mm (region 1) and 62 = eTeO for 5 < z < 10 mm (region 2). The bottom plate is held at constant potential V(0) = 0 and the electrostatic field between the plates is known to be —42X 0 < z < 5mm in7 = —22 3%, 5 < z < 10mm a) (10 pts) Determine er. b) (5 pts) Determine V(z = 10 mm) in volts. c) (5 pts) Determine the charge density p3 of the plate at z = 10 mm in C/m2. d) (10 pts) Determine the capacitance C of the structure described above in farads if the parallel plates at z = 0 and z = 10 mm were constrained to have finite areas A = W2 facing one another where W = 10 cm. In this calculation ignore the fringing fields. 2. A square loop of wire of some finite resistance R and 2 m2 surface area is located within a region of constant magnetic field B = 32 Wb/m2 as illustrated in the following diagram. 2 y a) (5 pts) What is the magnetic flux \11 through the loop when the orientation angle of the loop is 6 = 00? In your flux calculation make use of dS orientation shown in the diagram (dS points in 3 direction when 6 = O). b) (5 pts) What is the flux W as a function of angle 6 (using the same Sign convention as in part a)? c) (10 pts) Assuming that angle 6 is time varying at a rate of g3 = 7r %, what is the emf 6' around the loop at the instant when 9 = 45"? d) (5 pts) In what direction will a positive induced current I flow around the loop at the same instant? You may indicate your answer by drawing labeled arrows around the loop graphically. Justify your answer. e) (5 pts) What is I if resistance R of the wire loop is 2 Q? 3. We have on 2 = 0 plane a pulse of sheet current J 8(t) = Q f (t), where the function f (t), measured in A/m units, is specified below. Regions adjacent to the current sheet are vacuum. a) (10 pts) f (t) = 2t(u(t) —- u(t — 750)), which is a ramp of duration to starting at t = 0 and ending at t = to. Plot Jy(t) vs 25 over —to < t < 2750 if to = 2 us. Label all your axes carefully. b) (5 pts) What is the unit of the constant 2 in (a) so that J 3(t) has A/m units? c) (10 pts) Determine and plot Ey(z,t) and HA2, t) vs 75 for z = 1200 m. d) (15 pts) Determine and plot Ey(z, t) and Hm(z, t) vs 2 for t = 5ns. " 5"” ! a z 1 z 1 ;' 1 3 E ‘ ‘ “ ‘ a z 3 z , v z A, 5 A U ‘f A I ‘ k l l ‘ ‘ I l ‘ ; z < ; ' 1 ; : ..._»“auMW“.__aw._Mw,w.»M“WM.mmfi.wumw_mmu__m.«mmw.“Mmmvw‘mmwmmmWW...W“W‘WmMM‘WWWM«wflfik b>WCe>:éa«> ’ e ' “ ML. __1 _‘ I l‘ ‘ M ...
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